Appunti completi Fundamentals of astronomy and astrophysics

Stellar Structure Evolution

VO• CS: show peculiar absorption lines in their spectra• They are NOT grouped in early- solar and late-type according to their ageYerks spectral classification: two-dimensional system. It’s a luminosity-based class. Classificationwas based on the visual inspection of strong lines: the rate of ionisation is essentially determinedby the radiation field hence more luminous stars have deeper lines.

Lesson 10: Stellar structure evolutionWe will assume that a star is a huge sphere of gas without rotation, magnetic field or mass loss.+/- all stars are made of: end of their life.2 FORCES:• Gravity: pulls the stellar material towards the centre. Confines the gas in the star againstpressure expansion.• Pressure: due to thermal motions of the gas molecules tends to expand the gas outward.Support the star against gravitational collapseBalance everywhere -> hydrostatic equilibriumWRONG: Hydrostatic equilibrium is naturally realized without requiring any source of

energy

Free-fall timescale: time required for a star to collapse to a point if there is no outward pressure to counteract gravity

Kevin Helmholtz

time it takes for the object to radiate away a significant amount of its gravitational potential energy

Nuclear time scale

time to radiate the energy produced by the mass difference between the reactants and product of the nuclear reaction.

The mass of the nucleus is smaller than the sum of the masses of all its nucleons. The difference is called "binding energy per nucleon".

Radiation

energy transfer in the form of electromagnetic radiation

Convection

starts when radiation becomes inefficient I.e. photons cannot travel freely

Conduction

in stars is very inefficient, because electrons can travel only short distance

Vogt-Russell Theorem

the structure of a star, in hydrostatic and thermal equilibrium with all energy derived from nuclear reaction is uniquely determined by its MASS and the distribution of chemical elements throughout

point, the central temperature and pressure become high enough for nuclear fusion to start in thecore. The protostar becomes a main sequence star.

The hydrostatic equilibrium settles in during the protostar phase. The central temperature is too low for H fusion but enough for Li and deuterium burning.

Even the smallest perturbation can start a rotation motion in the cloud. For conservation of angular momentum, the cloud will become ellipsoidal, and the gravity of the thicker part will shape it as a disk.

Herbig-Haro objects are characterized by the expulsion of partially ionized gas on narrow jets, perpendicular to the accretion disk.

Energy is provided by hydrogen fusion in the core through PP-chains.

1. Stars have greater gravitational compression in their cores with increasing mass.
2. Greater thermal and radiation pressure is required to balance the greater gravitational compression.
3. The greater thermal pressure is provided by higher temperatures in the stellar core. Massive stars need higher core temperatures to be stable.
4. Higher energy production in the core means that more energy will leave the surface. Energy cannot be stored inside the star. Luminosity increases with mass.

The nuclear reaction rate is very sensitive to temperature even a slight increase in temperature makes the nuclear reaction occur at a much higher rate. Stars become brighter, hotter (surface and less dense with increasing mass (Main Sequence stars only). WRONG: The CNO cycle is less sensitive to temperature, so in massive stars nuclear reaction occur at much slower rate. Massive stars lives less because they burn a lot. They will explode into supernova. Connection in the core, radioactive transfer outside. Medium stars: core remains radiative, energy production spread over larger region, the envelope is convective -> the opacity is high. Radioactive and convective zones do not mix. Low mass star: low temperature, star fully convective so entirety of its mass can be used as fuel for fusion reactions, a lot of mix inside-outside. They stay in the Ms for extremely long times. Some of first LM stars are still in MS stage. They could live trillions of years. At some point the universe.will consist only of low mass, low brightness cold stars WRONG: At the end of their life, low mass stars will evolve into Carbon-Oxygen white dwarf and slowly cool down. Main sequence phase:

• Object with masses smaller than 0.08 solar masses are not massive enough to start Hydrogen Fusion
• The energy sustain the hydrodynamical equilibrium is provided by Hydrogen fusion in the core
• Stars more massive than 120 solar masses are predicted to be unstable, although exceptions have been observed
• WRONG: In the colour magnitude diagram, Main Sequence stars are randomly scattered all across the diagram

Lifetime of a star radiating like the sun:

• Chemical reaction or radioactivity are not efficient enough to justify the luminosity of the sun
• By radiating its gravitational potential energy a star could survive a few million years
• WRONG: Without any internal pressure to counterbalance gravity, a star would collapse in 15 minutes.
• WRONG: Nuclear reactions keep a star shining for billions of years.

star in balance for billions of years only if all its mass inconverted to energy

Carbon burning phase and beyond in stellar evolution

1. After carbon ignition, the star goes through a series of alternating nuclear burning/corecontraction cycles
2. Each nuclear burning phase is much quicker than the previous one, with silicon-burninglasting only few weeks
3. Carbon fusion in the core starts if the Carbon-Oxygen core has a mass greater thansolar masses1.06
4. WRONG: neutrino losses play only a minor contribution to the energy loss of the star, sincethey don't have any mass

Giant phase in stellar evolution:

• The turn-off is the point in the colour magnitude diagram where the star leaves the MainSequence to enter the giant phase
• When hydrogen is exhausted in the core, the star starts burning it in a shell surrounding aninert Helium core
• Giant stars are colder on the surface, but they are brighter because they have a largersurface than main sequence

Stars in the giant phase have the same size and luminosity, regardless of their mass during the main sequence phase

Asymptotic giant phase in stellar evolution (intermediate mass-stars)

• When helium in the core is exhausted, helium keeps burning in a shell leaving behind a carbon and oxygen core
• The star becomes unstable due to the presence of two shells with fusion reactions, Hydrogen and Helium respectively
• The star will lose the outer envelope into space, the expelled material takes the name of planetary nebula
• WRONG: the outcome of this phase will be a white dwarf either made of carbon and oxygen or just exclusively helium

Helium burning phase in stellar evolution (massive stars)

• Wolf-Rayet stars are exposed Hydrogen- or Helium-burning cores of massive stars, often surrounded by ejected material
• The Humphreys-Davidson limit sets the maximum luminosity of a star before becoming unstable for radiation pressure
• Luminous blue variables

undergo violent outburst with important mass loss and large excursions in luminosity • WRONG: The blue super giant phase is extremely slow, and the probability of observing it in the Hertzprung-Russel diagram is high Nuclear fusion reactions: • The proton-proton III chain, even if marginal, explains the very high energy neutrinos from the sun • In the sun 99% of the energy is produced by the proton-proton chain, and 91% from ppI chain 19 • The Carbon-Nitrogen-Oxygen cycle is predominant only for stars more massive than the sun • WRONG: The CNO cycle causes a noticeable variation of the abundance of "metals" in the core of the star Collapse of a massive star: • The star collapses on its core and then material bounces back in a very energetic supernova explosion • Pre-supernova structure is formed by an Iron core surrounded by shells of progressively lighter elements • Iron has the highest binding energy per nucleon, so its fusion cannot produce any

energy• WRONG: Neutronization and photo-disintegration increase the pressure in the core, slowing down the collapse

Lesson 11: Compact objects (low and medium-mass stars)

Normal gas:• thermal effects dominate, increasing the temperature will increase the pressure. When two atoms approach each other, the electrons in one atom repel the electrons in the other atom via electric forces.

• Under high densities the gas becomes a collection of positively charged ions floating in a sea of electrons, which have been stripped from the nuclei. The electron degeneracy pressure is independent of temperature because it is related to the repulsive force.

• At even higher density, electrons and protons merge together to form a neutron sea. The neutron degeneracy pressure is similar to the E.D.P but it is stronger.

White dwarf: when there is no nuclear reaction in the core, density increases until the gas becomes a collection of positively charged ions floating in a sea of electrons which have

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Been stripped from the nuclei. Compression does not lead to heating and expansion as in regular stars: . Temperature does not depend on density. WDS are hot because of previous stages of stellar evolution not because of their degenerate status.

Other characteristics:

• Mainly composed by O and C, with a thin H and He atmosphere
• Initially hot but they are "dim" (low luminosity) because of small size
• No source of energy, they will gradually cool and become black dwarfs
• When cools down, carbon assumes a crystalline configuration similar to those of diamonds
• Matter forms an accretion disk around the WD and eventually fall on it
• Compression does not lead to heating an expansion as in regular stars: increases the mass causes smaller radius